ApCoCoA-1:NC.Deg

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NC.Deg

The (standard) degree of a polynomial in non-commutative polynomial rings.

Syntax

NC.Deg(F:LIST):INT

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Please set ring environment coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

  • @param F: a polynomial in K<X>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].

  • @return: an INT which represents the (standard) degree of F. If F=0, the function returns 0.

Example

NC.SetX(<quotes>abc</quotes>);
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
NC.Deg(F);
3
-------------------------------
NC.Deg([]); -- 0 polynomial
0
-------------------------------

See also

NC.SetOrdering

Introduction to CoCoAServer